Evaluation method for deformation caused by excavation with two fixed ends of pile foundation

Abstract

The invention provides a method for evaluating deformation caused by excavation with two fixed ends of a pile foundation, and provides a method for evaluating deformation caused by excavation with two fixed ends of the pile foundation by combining a Fourier series method under the conditions that the boundary condition of the pile foundation can be simplified into the pile foundation with two fixed ends under the conditions of an end bearing pile, a socketed pile, a pile top embedded bearing platform and the like. The method is used for calculating pile foundation horizontal displacement and internal force caused by shield adjacent pile foundation construction, compared with a numerical simulation method, physical quantities needing to be calculated can be obtained by substituting corresponding calculation parameters, the calculation process is simple and convenient, and compared with a theoretical method with the help of a numerical method, the calculation efficiency is improved. According to the method, other undetermined coefficients can be further obtained only by solving the binary linear equation related to the pile end shearing force QO and QL, the calculation efficiency is high, and an effective theoretical method is provided for safety risk evaluation of an existing structure in shield adjacent pile foundation construction.

Description

Technical Field

[0001] The invention relates to the technical field of tunnel engineering design, and in particular to a method for evaluating deformation caused by excavation of a pile foundation with both ends fixed. Background Art

[0002] In the context of large-scale construction of urban rail transit, the excavation of new shield tunnels will inevitably encounter the construction of existing pile foundations nearby, causing deformation of the pile foundations. Considering that the displacement constraints at both ends of the pile foundations such as end-bearing piles and rock-embedded piles can be simplified to fixed constraints, the current research on the deformation assessment method caused by excavation with fixed constraints at both ends of the pile foundation mainly relies on numerical methods such as the finite difference method, and there are few studies on analytical methods. Compared with the calculation method based on numerical methods, the analytical method has higher calculation efficiency and more stable algorithm. Therefore, it is necessary to conduct research on the evaluation method of the deformation of the pile foundation with fixed constraints at both ends caused by the excavation of new shield tunnels. Summary of the invention

[0003] The purpose of the present invention is to provide a method for evaluating the deformation caused by excavation with both ends of a pile foundation fixed. Taking into account the situation that the displacement constraints at both ends of pile foundations such as end-bearing piles and rock-embedded piles can be simplified to fixed constraints, according to the stratum displacement caused by shield tunnel excavation, based on the dual-parameter foundation model theory and combined with the basic physical and mechanical parameters of the pile foundation and soil, a method for evaluating the deformation caused by excavation with both ends of a pile foundation fixed is derived.

[0004] In order to achieve the above object, the technical solution adopted by the present invention is: a method for evaluating deformation caused by excavation with both ends of a pile foundation fixed, the calculation method comprising the following steps: Step 1: Use the Fourier series method to solve the bending deformation of the pile foundation under the influence of shield tunnel excavation. The dual-parameter foundation model adopts the Vlasov foundation model. The existing pile foundation is assumed to be an elastic foundation beam, which satisfies the plane section assumption. The horizontal displacement control differential equation of the existing pile foundation caused by shield tunnel excavation is: Where: E is the elastic modulus of the existing pile foundation; I is the interface moment of inertia of the existing pile foundation; w is the horizontal displacement of the existing pile foundation, with the side away from the tunnel excavation as positive; z is the coordinate along the axis of the existing pile foundation, with the top of the pile as the origin z=0; t is the load transfer rate; B is the diameter of the pile foundation; k is the stiffness coefficient of the soil on the side of the pile; U is the horizontal displacement of the stratum at the pile position caused by the shield tunnel excavation; Step 2: Determine the calculation formula for the horizontal displacement of the fixed pile foundations at both ends caused by shield tunnel excavation: Where w0 is the cosine series constant of the pile foundation horizontal displacement function; w n is the cosine series term of the pile foundation horizontal displacement function; L is the calculated length of the pile foundation; QO , Q L are the shear forces at the pile top and pile bottom respectively; Step 3: Determine the calculation formula for the bending moment and shear force of the fixed pile foundations at both ends caused by shield tunnel excavation: Where, M is the bending moment of the pile foundation; Q is the shear force of the pile foundation; Step 4: The expressions of pile foundation horizontal displacement w, pile foundation bending moment M, and pile foundation shear force Q in steps 1-3 contain the unknown coefficients w0 and w n , Q O , Q L , where the unknown coefficients w0, w n Determined by the following formula: Where U0 is the constant term after the cosine series expansion of the known formation displacement function U(z), that is, α0、α n , β0, β n , γ n is the comprehensive coefficient; Undetermined coefficient Q O , Q L Determined by the following formula: In the formula, S1~S6 are comprehensive coefficients.

[0005] Preferably, for the Vlasov foundation model, there are: Among them, Es is the elastic modulus of the soil; υs is the Poisson's ratio of the soil; He is the thickness of the foundation elastic layer, which is 2.5 times the pile diameter D; h is the function of the displacement along the horizontal direction, which is

[0006] Preferably, for the Vlasov foundation model, there are:

[0007] Preferably, for the Vlasov foundation model, the soil displacement field analytical formula proposed by Loganathan is adopted: Among them, ε0 is the stratum loss rate; x0 is the horizontal distance from the pile foundation axis to the tunnel axis; R is the tunnel excavation radius; H is the burial depth of the tunnel center.

[0008] Preferably, the comprehensive coefficients α0, αn, β0, βn, and γn are determined by the following formula: in, The known functions are The coefficients of the cosine series expansion are U n is the series coefficient after the cosine series expansion of the known formation displacement function U(z), that is,

[0009] Preferably, the comprehensive coefficients S1 to S6 are determined by the following formula:

[0010] The beneficial effects of the present invention are:

[0011] In this scheme, the boundary conditions of the pile foundation can be simplified to pile foundations fixed at both ends for end-bearing piles, rock-embedded piles, and pile tops embedded in caps. Combined with the Fourier series method, a deformation assessment method caused by excavation with both ends of the pile foundation fixed is proposed to calculate the horizontal displacement and internal force of the pile foundation caused by the construction of the shield adjacent to the pile foundation. Compared with the numerical simulation method, the required physical quantities can be obtained by substituting the corresponding calculation parameters, and the calculation process is simple. Compared with the theoretical method with the help of numerical methods, this method only needs to solve the binary linear equation related to the pile end shear force QO and QL to further obtain other unknown coefficients. The calculation efficiency is high, which provides an effective theoretical method for the safety risk assessment of existing structures adjacent to the shield construction. BRIEF DESCRIPTION OF THE DRAWINGS

[0012] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative work.

[0013] Figure 1 This is a simplified diagram for calculating the horizontal displacement of existing pile foundations caused by the construction of tunnel adjacent to pile foundations in an embodiment of the present invention.

[0014] Figure 2 The figure is a comparison chart of the pile foundation horizontal displacement calculated in the embodiment of the present invention and the calculation results in the existing literature.

[0015] Figure 3 It is a comparison chart of the pile foundation bending moment calculated in the embodiment of the present invention and the calculation results in the existing literature.

[0016] Figure 4 It is a comparison chart of the pile foundation shear force calculated in the embodiment of the present invention and the calculation results of the existing literature. DETAILED DESCRIPTION

[0017] The present invention will be further described in detail below in conjunction with the accompanying drawings and specific embodiments.

[0018] The present invention discloses a method for evaluating deformation caused by excavation of a pile foundation with both ends fixed. In order to make the purpose of this application and the technical solution clearer, combined with the existing literature, namely, Sun Yingjie, Shi Chenghua, Wang Zuxian, etc., the analytical solution of the response of adjacent pile foundation induced by tunnel construction considering the actual constraints at both ends, the data and calculation parameters and the calculation diagram are as follows Figure 1 As shown, the present application is further described.

[0019] After the tunnel is constructed near the existing pile foundation, the stratum loss rate ε0 is 2.5%, the soil elastic modulus Es is 24MPa, the Poisson's ratio υs is 0.5, the tunnel diameter D is 6m, the pile foundation elastic modulus E is 30GPa, the pile diameter B is 0.5m, the pile length L is 25m, the tunnel center burial depth H is 20m, and the horizontal distance x0 between the tunnel axis and the pile foundation axis is 4.5m. The calculation diagram is as follows: Figure 1 As shown, the two ends of the pile foundation are fixed constraints.

[0020] Step 1: For the pile foundation boundary conditions and load conditions described in this example, the pile foundation is regarded as an elastic foundation beam on the Vlasov foundation model. The control differential equation for the horizontal displacement of the existing pile foundation caused by tunnel excavation is: Where: E is the elastic modulus of the existing pile foundation, Pa; I is the interface moment of inertia of the existing pile foundation, m 4 ; w is the horizontal displacement of the existing pile foundation, m, with the side away from the tunnel excavation as positive; z is the coordinate along the axis of the existing pile foundation, m, with the top of the pile as the origin z=0; B is the diameter of the pile foundation, m; t is the load transfer rate, N / m.

[0021] For the Vlasov foundation model, we have: Among them, Es is the elastic modulus of the soil; υs is the Poisson's ratio of the soil; He is the thickness of the foundation elastic layer, which is 2.5 times the pile diameter D; h is the function of the displacement along the horizontal direction, i.e., the x direction, which is

[0022] k is the stiffness coefficient of the soil around the pile, Pa / m. For the Vlasov foundation model, it is:

[0023] U is the horizontal displacement of the stratum at the pile position caused by shield tunnel excavation, and the analytical formula of soil displacement field proposed by Loganathan is taken as: Among them, ε0 is the stratum loss rate; x0 is the horizontal distance from the pile foundation axis to the tunnel axis, m; R is the tunnel excavation radius, m; H is the burial depth of the tunnel center, m.

[0024] Step 2: Determine the calculation formula for the horizontal displacement of the fixed pile foundations at both ends caused by shield tunnel excavation: Where w0 is the cosine series constant of the pile foundation horizontal displacement function; w n is the cosine series term of the pile foundation horizontal displacement function; L is the calculated length of the pile foundation, m; Q O , Q L are the shear forces at the pile top and pile bottom, N respectively.

[0025] Step 3: Determine the calculation formula for the bending moment and shear force of the fixed pile foundations at both ends caused by shield tunnel excavation: Where M is the bending moment of the pile foundation, N·m; Q is the shear force of the pile foundation, N.

[0026] Step 4: The expressions of pile foundation horizontal displacement w, pile foundation bending moment M, and pile foundation shear force Q in steps 1-3 contain the unknown coefficients w0, wn, QO, and QL, where the unknown coefficients w0 and wn are determined by the following formula:

[0027] Where U0 is the constant term after the cosine series expansion of the known formation displacement function U(z), that is, α0, αn, β0, βn, and γn are comprehensive coefficients, which are determined by the following formula:

[0028] Among them, φ1,0, φ1,n, φ2,0, φ2,n are known functions respectively. The coefficients of the cosine series expansion are Un is the series coefficient of the cosine series expansion of the known formation displacement function U(z), that is,

[0029] The undetermined coefficients QO and QL are determined by the following formula:

[0030] In the formula, S1~S6 are comprehensive coefficients, which are determined by the following formula:

[0031] Substitute the known calculation parameters into the above formula to obtain the unknown coefficients w0, wn, QO, QL, and then obtain the pile foundation horizontal displacement w(z), bending moment M(z) and shear force Q(z) caused by the adjacent construction of the tunnel. The results are as follows: Figure 2 to Figure 4As shown in the figure, in order to verify the correctness of the calculation method of the present invention, the calculation results of the analytical solution of the response of adjacent pile foundation induced by tunnel construction considering the actual constraints at both ends by Sun Yingjie, Shi Chenghua, Wang Zuxian, etc. are compared. It can be seen that the calculation results of this embodiment are basically consistent with the calculation results of the existing literature, which proves the correctness of the calculation method of the present invention. In the literature, the calculation of pile foundation displacement and internal force is carried out by means of finite difference method. Compared with the calculation method in the literature, the calculation method of the present invention only needs to solve the two-variable linear equation to obtain the unknown boundary conditions of the control differential equation, and the calculation efficiency is significantly improved.

[0032] It should be noted that the parts not described in detail in the above embodiments are all prior art.

[0033] The above description is only a preferred embodiment of the present invention and does not constitute any form of limitation to the present invention. Although the present invention has been disclosed as a preferred embodiment as above, it is not intended to limit the present invention. Any technician familiar with the profession can make some changes or modifications to equivalent embodiments of equivalent changes using the technical contents disclosed above without departing from the scope of the technical solution of the present invention. However, any simple modifications, equivalent changes and modifications made to the above embodiments based on the technical essence of the present invention without departing from the content of the technical solution of the present invention should be covered within the protection scope of the present invention.

Claims

1. A method for evaluating deformation caused by excavation of a pile foundation with both ends fixed, characterized in that: The calculation method comprises the following steps: Step 1: Use the Fourier series method to solve the bending deformation of the pile foundation under the influence of shield tunnel excavation. The dual-parameter foundation model adopts the Vlasov foundation model. The existing pile foundation is assumed to be an elastic foundation beam, which satisfies the plane section assumption. The horizontal displacement control differential equation of the existing pile foundation caused by shield tunnel excavation is: Where: E is the elastic modulus of the existing pile foundation; I is the interface moment of inertia of the existing pile foundation; w is the horizontal displacement of the existing pile foundation, with the side away from the tunnel excavation as positive; z is the coordinate along the axis of the existing pile foundation, with the top of the pile as the origin z=0; t is the load transfer rate; B is the diameter of the pile foundation; k is the stiffness coefficient of the soil on the side of the pile; U is the horizontal displacement of the stratum at the pile position caused by the shield tunnel excavation; Step 2: Determine the calculation formula for the horizontal displacement of the fixed pile foundations at both ends caused by shield tunnel excavation: Where w0 is the cosine series constant of the pile foundation horizontal displacement function; w n is the cosine series term of the pile foundation horizontal displacement function; L is the calculated length of the pile foundation; Q O , Q L are the shear forces at the pile top and pile bottom respectively; Step 3: Determine the calculation formula for the bending moment and shear force of the fixed pile foundations at both ends caused by shield tunnel excavation: Where, M is the bending moment of the pile foundation; Q is the shear force of the pile foundation; Step 4: The expressions of pile foundation horizontal displacement w, pile foundation bending moment M, and pile foundation shear force Q in steps 1-3 contain the unknown coefficients w0 and w n , Q O , Q L , where the unknown coefficients w0, w n Determined by the following formula: Where U0 is the constant term after the cosine series expansion of the known formation displacement function U(z), that is, α0, α n , β0, β n , γ n is the comprehensive coefficient; Undetermined coefficient Q O , Q L Determined by the following formula: In the formula, S1~S6 are comprehensive coefficients.

2. The method for evaluating deformation caused by excavation of a pile foundation with both ends fixed according to claim 1, characterized in that: For the Vlasov foundation model, we have: Among them, E s is the elastic modulus of soil; s is the Poisson's ratio of soil; H e is the thickness of the foundation elastic layer, which is 2.5 times the pile diameter D; h is the function of displacement along the horizontal direction, which is 3. The method for evaluating deformation caused by excavation of a pile foundation with both ends fixed according to claim 2, characterized in that: For the Vlasov foundation model, we have:

4. The method for evaluating deformation caused by excavation of a pile foundation with both ends fixed according to claim 3, characterized in that: For the Vlasov foundation model, the analytical formula of soil displacement field proposed by Loganathan is adopted: Among them, ε0 is the stratum loss rate; x0 is the horizontal distance from the pile foundation axis to the tunnel axis; R is the tunnel excavation radius; H is the burial depth of the tunnel center.

5. The method for evaluating deformation caused by excavation of a pile foundation with both ends fixed according to claim 4, characterized in that: The comprehensive coefficients α0, α n , β0, β n , γ n Determined by the following formula: in, The known functions are The coefficients of the cosine series expansion are U n is the series coefficient after the cosine series expansion of the known formation displacement function U(z), that is, 6. The method for evaluating deformation caused by excavation of a pile foundation with both ends fixed according to claim 5, characterized in that: The comprehensive coefficients S1 to S6 are determined by the following formula:

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